Troops in the new Republican Guard unit began training six months ago for "protecting higher government officials and their family, from any form of aggression by ill-intentioned forces," Fana announced on its website.
The formation of the specialised unit followed the explosion of a hand grenade in the middle of a huge crowd of people who had gathered in the capital Addis Ababa to hear Abiy speak on June 23. Two people were killed and scores injured.
Some observers believe the prime minister was the intended target of the grenade attack, but he was not harmed.
After taking office in April, Abiy gained public support with promises of reform to promote national unity after years of hardline rule.
He has freed thousands of jailed dissidents and journalists and cemented peace with neighbouring Eritrea, after a 1998-2000 war that left a legacy of distrust.
Ethiopia had an Imperial Guard during the reign of Emperor Haile Selassie, but that military unit was disbanded after he was ousted in an army coup in September 1974.
A recent upsurge in the number of ethnic confrontations in Addis Ababa and of clashes in remote regions has aroused fears that the second most populous nation in Africa after Nigeria faces renewed violence.
According to a 2017 estimate by the UN Department of Economic and Social Affairs, the population is about 102.4 million. The Horn of Africa nation is home to dozens of distinct ethnic groups.